A003190 Number of connected 2-plexes. (Formerly M3121)

1, 0, 1, 3, 29, 2101, 7011181, 1788775603301, 53304526022885278403, 366299663378889804782330207902, 1171638318502622784366970315262493034215728, 3517726593606524901243694560022510194169866584119717555335

Offset

1,4

Comments

The Palmer reference (incorrectly) has a(7)=7011349, a(8)=1788775603133, a(9)=53304526022885278659. - Sean A. Irvine, Mar 05 2015

Also connected 3-uniform hypergraphs on n vertices. - Gus Wiseman, Feb 23 2019

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..12.

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

E. M. Palmer, On the number of n-plexes, Discrete Math., 6 (1973), 377-390.

Formula

Inverse Euler transform of A000665. - Sean A. Irvine, Mar 05 2015

Example

From Gus Wiseman, Feb 23 2019: (Start)
Non-isomorphic representatives of the a(5) = 29 2-plexes:
  {{125}{345}}
  {{123}{245}{345}}
  {{135}{245}{345}}
  {{145}{245}{345}}
  {{123}{145}{245}{345}}
  {{124}{135}{245}{345}}
  {{125}{135}{245}{345}}
  {{134}{235}{245}{345}}
  {{145}{235}{245}{345}}
  {{123}{124}{135}{245}{345}}
  {{123}{145}{235}{245}{345}}
  {{124}{134}{235}{245}{345}}
  {{134}{145}{235}{245}{345}}
  {{135}{145}{235}{245}{345}}
  {{145}{234}{235}{245}{345}}
  {{123}{124}{134}{235}{245}{345}}
  {{123}{134}{145}{235}{245}{345}}
  {{123}{145}{234}{235}{245}{345}}
  {{124}{135}{145}{235}{245}{345}}
  {{125}{135}{145}{235}{245}{345}}
  {{135}{145}{234}{235}{245}{345}}
  {{123}{124}{135}{145}{235}{245}{345}}
  {{124}{135}{145}{234}{235}{245}{345}}
  {{125}{135}{145}{234}{235}{245}{345}}
  {{134}{135}{145}{234}{235}{245}{345}}
  {{123}{124}{135}{145}{234}{235}{245}{345}}
  {{125}{134}{135}{145}{234}{235}{245}{345}}
  {{124}{125}{134}{135}{145}{234}{235}{245}{345}}
  {{123}{124}{125}{134}{135}{145}{234}{235}{245}{345}}
(End)

Crossrefs

Column k=3 of A301924.

Cf. A000665 (unlabeled 3-uniform), A025035, A125791 (labeled 3-uniform), A289837, A301922, A302374 (labeled 3-uniform spanning), A302394, A306017, A319540, A320395, A322451 (unlabeled 3-uniform spanning), A323292-A323299.

Sequence in context: A182385 A255597 A319637 * A322451 A213792 A133663

Adjacent sequences: A003187 A003188 A003189 * A003191 A003192 A003193

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

a(7)-a(9) corrected and extended by Sean A. Irvine, Mar 05 2015

Status

approved